1. Field of the Invention
The present invention relates to a method for analyzing on a computer, the plastic deformation process of a rotary formed body in rotary metal forming such as disk rolling, spinning, curling and rotary forging, as in for example the metal forming of a formed and fabricated materials having a ring shape in ring rolling. In particular, the invention relates to a technique for performing numerical simulation by modeling a rotary formed body using a rigid plastic finite element analysis method.
2. Description of the Related Art
Heretofore, with a background of increased speed in computer processing and advancement in finite element analysis methods, improvements in efficiency of process design is advancing due to performing virtual numerical simulation by computer before performing actual trials of metal working processes.
However, with respect to the processing methods for plastic deformation by repeating localized contact with a rotary formed body, such as for example in the ring rolling process for performing metal forming of a formed and fabricated materials having a ring shape, multiple contact and withdrawal of the forming roll and the rotary formed body is repeated from the start of forming to completion of forming. Therefore there are cases where in numerical simulation using the finite element analysis method, considerable computation time is necessary.
For example, in the rigid plastic finite element analysis method, in a method for modeling the entire rotary formed body of a ring shape or the like, and moreover in a method for providing relatively fine finite elements in a predetermined zone inside the roll gap, as well as modeling the entire body (for example, N. S. KIM, S. MACHIDA and S. KOBAYASHI, Ring Rolling Process Simulation by the Three Dimensional Finite Element Method. Int. J. Mach. Tools Manufact. 30, 569 (1990)), it is possible to reproduce highly accurately the complex plastic deformation in three dimensions of the rotary formed body. However, since the numerical simulation is also executed for the zone outside of the roll gap interior which has only been slightly deformed, there is the problem that considerable computation time is necessary.
On the other hand, for example as with a two-dimensional cross-section approximation, essentially it is possible to considerably shorten the computation time with a method which handles the plastic deformation process in three dimensions with a two dimensional and an expanded two dimensional model. However, because there are many assumptions related to transformations for making this applicable when two dimensionalized, the accuracy with respect to the analysis of the complex shape is low, and the influence of for example the roll diameter of the forming roll and the ring radius of the rotary formed body can not be taken into consideration. Hence a problem arises in that the accuracy of the plastic strain obtained as the result of the analysis is low.
Therefore, there is known a numerical-simulation method using a partial model for modeling by finite elements which subdivide only a predetermined zone for producing the main plastic deformation such as inside of the roll gap in the ring rolling (for example, D. Y. YANG, and K. H. KIM, Rigid-Plastic Finite Element Analysis of Plane Strain Ring Rolling. Int. J. Mech. Sci. 30, 571 (1988) and D. Y. YANG, K. H. KIM and J. B. HAWKYARD, Simulation of T-Section Profile Ring Rolling by the 3-D Rigid-Plastic Finite Element Method. Int. J. Mech, Sci. 33, 541 (1991)).
Incidentally, in the numerical-simulation method using the above-mentioned partial model, it is possible to shorten the computation time, and to reproduce highly accurately complex plastic deformation in three dimensions. However, if the velocity boundary conditions at the boundary (imaginary cutting plane) of the zone that has been modeled and the zone that has not been modeled are not appropriately set, a problem arises in that high accuracy analysis results can not be obtained.
For example, in the numerical-simulation method according to the above-mentioned related art, the velocity boundary conditions are only set based on the assumption that the boundary cross-sections set in the rotary formed body have rigid body rotation in respective independent peripheral directions (circumferential directions) in only two cutting planes. Hence a problem arises in that, for the plastic deformation produced at the time of the forming process, it is not possible to reproduce for example the plastic deformation for where the rotary formed body is rolled out in the roll gap and elongates in the circumferential direction.
Moreover, in the numerical-simulation method according to the above mentioned related art, since the ring rolling process being essentially a transient deformation process, is handled as divided steady deformation, the entire process can not be reproduced as a continuous phenomena. Hence a problem arises in that the accuracy of the simulation can not be improved.